List questions from stochastic-calculus

Published on 09 Apr 2026 - 17:46

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Why is a stochastic integral w.r.t a martingale always a local martingale?

Published on 02 Apr 2026 - 23:20

63

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Why $B_T\circ\theta_S=B_T$ with $(B_t)$ Brownian motion

Published on 07 Oct 2015 - 0:53

11k

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Integral of a Gaussian process

Published on 11 Apr 2026 - 18:55

39

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Show that $\mathbb{E}Y_t^3 =0$

Published on 09 Oct 2015 - 13:30

99

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Why writing $[X,Y]_t$ as $dX_t dY_t$ is so called "abuse of notation"

Published on 02 Apr 2026 - 23:21

72

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Prove that: $E[\int^{\tau}_{0} f(t)d\omega(t)]=0$ and $E\mid \int^{\tau}_{0} f(t)d\omega(t)\mid^2=E[\int^{\tau}_{0} f^2(t)dt]$.

Published on 08 Apr 2026 - 6:39

73

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question about martingale inequality (similar to the condition of submartingale convergence)

Published on 05 Apr 2026 - 11:09

291

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SDE solution with $\mu_t$ a bounded integral

Published on 29 Mar 2026 - 9:12

170

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laplace transform of smirnov density, i.e. how to calculate this integral?

Published on 07 Apr 2026 - 17:42

285

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Solving a Stochastic PDE with two variables in time

Published on 01 Apr 2026 - 14:08

53

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Why isn't this stochastic integral trivial?

Published on 03 Apr 2026 - 0:53

30

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Proving linearity of a subspace of $L^2$

Published on 15 Oct 2015 - 3:07

119

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How to obtain this result using Ito's Lemma?

Published on 15 Oct 2015 - 14:36

1.4k

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Using Fubini's Theorem in Stochastic Calculus

Published on 28 Mar 2026 - 10:37

List Question

Quadratic Variation of Brownian motion indexed by cadlag increasing function

Why is a stochastic integral w.r.t a martingale always a local martingale?

Why $B_T\circ\theta_S=B_T$ with $(B_t)$ Brownian motion

Integral of a Gaussian process

Show that $\mathbb{E}Y_t^3 =0$

Why writing $[X,Y]_t$ as $dX_t dY_t$ is so called "abuse of notation"

Prove that: $E[\int^{\tau}_{0} f(t)d\omega(t)]=0$ and $E\mid \int^{\tau}_{0} f(t)d\omega(t)\mid^2=E[\int^{\tau}_{0} f^2(t)dt]$.

question about martingale inequality (similar to the condition of submartingale convergence)

SDE solution with $\mu_t$ a bounded integral

laplace transform of smirnov density, i.e. how to calculate this integral?

Solving a Stochastic PDE with two variables in time

Why isn't this stochastic integral trivial?

Proving linearity of a subspace of $L^2$

How to obtain this result using Ito's Lemma?

Using Fubini's Theorem in Stochastic Calculus

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